Problem: Simplify the following expression: $\sqrt{12}-\sqrt{48}+\sqrt{75}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{12}-\sqrt{48}+\sqrt{75}$ $= \sqrt{4 \cdot 3}-\sqrt{16 \cdot 3}+\sqrt{25 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{3}-\sqrt{16} \cdot \sqrt{3}+\sqrt{25} \cdot \sqrt{3}$ $= 2\sqrt{3}-4\sqrt{3}+5\sqrt{3}$ Finally, simplify by combining the terms. $= ( 2 - 4 + 5 )\sqrt{3} = 3\sqrt{3}$